Problem Set Week 4 four Confidence Intervals and Chi Square (Chs 11 - 12)

Problem Set Week 4 four Confidence Intervals and Chi Square (Chs 11 - 12)

For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements.  Use .05 for your significance level in making your decisions.

For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.

1

Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender.  

Interpret the results.  How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?

Interpretation:

2

Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population.   

How does this compare to the findings in week 2, question 2?

Difference

St Err.

T value

Low

to

High

Can the means be equal?

How does this compare to the week 2, question 2 result (2 sampe t-test)?

Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples?

3

We found last week that the degree values within the population do not impact compa rates. 

This does not mean that degrees are distributed evenly across the grades and genders.

Do males and females have athe same distribution of degrees by grade?

(Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.)

What are the hypothesis statements:

Ho:

Ha:

Note:  You can either use the Excel Chi-related functions or do the calculations manually.

Data input tables - graduate degrees by gender and grade level

If desired, you can do manual calculations per cell here.

For this exercise - ignore the requirement for a correction factor

for cells with expected values less than 5.

Interpretation:

What is the value of the chi square statistic:

What is the p-value associated with this value:

Is the p-value <0.05?

Do you reject or not reject the null hypothesis:

If you rejected the null, what is the Cramer's V correlation:

What does this correlation mean?

What does this decision mean for our equal pay question:

4

Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern

within the population?

What are the hypothesis statements:

Do manual calculations per cell here (if desired)

OBS COUNT - m

OBS COUNT - f

What is the value of the chi square statistic:

What is the p-value associated with this value:

Is the p-value <0.05?

Do you reject or not reject the null hypothesis:

If you rejected the null, what is the Phi correlation:

What does this correlation mean?

What does this decision mean for our equal pay question:

5.      How do you interpret these results in light of our question about equal pay for equal work?